None.
Not applicable.
The invention presents the description of a new measurement based model that provides the basis for a theoretical description of the behavior of a power plant steam surface condenser performance under the influence of air in-leakage. The measurement is a quantification of properties of the water vapor and non-condensable gas mixture flowing in the vent line between the condenser and the exhauster. These properties are used, along with condenser measurements and operating conditions, to identify gas mixture properties inside the condenser. This model then is used to predict important condenser performance and behavior, which is compared to plant measurements and observations to confirm model validity. The measurement is shown to be compatible with requirements for modern power plant information systems supporting O and M, plant life, asset management and predictive maintenance. Innovative design modifications of present condenser systems and new systems and measurements are anticipated.
In 1963, Professor R. S. Silver (R. S. Silver, xe2x80x9cAn Approach to a General Theory of Surface Condensersxe2x80x9d, Proceedings of the Institution of Mechanical Engineers, Vol. 178 Pt 1, No. 14, London, pp. 339-376, 1963-64) published a stimulating paper dealing with the general theory of surface condensers, wherein it was stated that, xe2x80x9cIt is well known to all operators and designers of condensing plants that the presence of a small proportion of air in the vapor can reduce the heat transfer performance in a marked manner.xe2x80x9d In a recent publication by EPRI (R. E. Putman, Condenser In-Leakage Guideline, EPRI, TR-112819, January, 2000) on the effects of air ingress, it is stated, xe2x80x9c . . . but the presence of even small amounts of air or other non-condensables in the shell space can cause a significant reduction in the effective heat transfer coefficient.xe2x80x9d In effect, for thirty-eight years, this understanding has remained entrenched and unchanged. In neither of these publications, nor any other publication or known paper, has a quantifiable amount of air in-leakage into an operating condenser resulted in a measured change in condenser performance that can be defined by a comprehensive theoretical treatment in support of these statements.
The currently accepted description of a condenser and the formulas for determining its performance are discussed below. The illustration in FIG. 1 represents the temperature profile of cooling water passing through tubes in a condenser. The following abbreviations apply to FIG. 1 and are used herein:
THW is the hotwell temperature;
Tv is the vapor temperature, which can be set equal to the hotwell temperature THW; 
Tcw1 and Tcw2 are the inlet and outlet circulating water temperatures, respectively;
TTD is the terminal temperature difference;
xcex94Tcw is the rise in circulating water temperature; and
xcex94Tlm is the Grashof logarithmic mean temperature difference, which is the mean temperature driving force for heat flow between the exhaust steam vapor and cooling water in the condenser tubes.
The relationship between xcex94Tlm and other variables in FIG. 1 (in which all temperatures are in xc2x0 F.) is as follows:                               Δ          ⁢                      xe2x80x83                    ⁢                      T                          l              ⁢                              xe2x80x83                            ⁢              m                                      =                                            T              cw2                        -                          T              cw1                                            ln            ⁡                          (                                                                    T                    v                                    -                                      T                    cw1                                                                                        T                    v                                    -                                      T                    cw2                                                              )                                                          Eq        .                  xe2x80x83                ⁢        1            
Equation 1 in turn can be written as:                               Δ          ⁢                      xe2x80x83                    ⁢                      T                          l              ⁢                              xe2x80x83                            ⁢              m                                      =                              Δ            ⁢                          xe2x80x83                        ⁢                          T              cw                                            ln            ⁡                          (                              1                +                                                      Δ                    ⁢                                          xe2x80x83                                        ⁢                                          T                      cw                                                        TTD                                            )                                                          Eq        .                  xe2x80x83                ⁢        2            
Since xcex94Tcw is due to a steam load, Q (BTU/hr), from the turbine requiring energy removal sufficient to convert it to condensate, one also can write the following equations:
Q={dot over (m)}cwcpxcex94Tcw(Heat load to the circulating water)xe2x80x83xe2x80x83Eq.3
and,
Q={dot over (m)}shfg(Heat load from steam condensation)xe2x80x83xe2x80x83Eq.4
where,
{dot over (m)}cw (lbs/hr) is the mass flow rate of circulating water,
cp (BTU/lbxc2x7xc2x0 F.) the specific heat of water,
{dot over (m)}s (lbs/hr) the mass flow rate of steam, and
hfg (BTU/lb) the enthalpy change (latent heat of vaporization).
Combining Equations 3 and 4, yields the following equation:                               Δ          ⁢                      xe2x80x83                    ⁢                      T            cw                          =                                                            m                .                            s                        ⁢                          h              fg                                                                          m                .                            cw                        ⁢                          c              p                                                          Eq        .                  xe2x80x83                ⁢        5            
which defines the rise in circulating water temperature in terms of mass ratio of steam flow to circulating water flow and two identifiable properties. Consistent with good engineering heat transfer practice in describing heat exchangers, Q is related to the exposed heat transfer surface area A, and xcex94Tlm, with a proportionality factor characteristically called the heat transfer coefficient, U. This relationship is given by:
Q=UAxcex94Tlmxe2x80x83xe2x80x83Eq.6
Combining equation (6) with equations (2) and (3), yields the following equation:                                           m            .                    cw                =                              U            ⁢                          xe2x80x83                        ⁢            A                                              c              p                        ⁢                          ln              ⁡                              (                                  1                  +                                                            Δ                      ⁢                                              xe2x80x83                                            ⁢                                              T                        cw                                                              TTD                                                  )                                                                        Eq        .                  xe2x80x83                ⁢        7            
which, following rearrangement, becomes:                     TTD        =                              Δ            ⁢                          xe2x80x83                        ⁢                          T              cw                                            (                                          l                                  (                                      UA                                                                                            m                          .                                                cw                                            ⁢                                              c                        p                                                                              )                                            -              1                        )                                              Eq        .                  xe2x80x83                ⁢        8            
Since cp is constant, {dot over (m)}cw and xcex94Tcw held constant through a fixed load Q, and with A assumed constant, the terminal temperature difference becomes only a function of U, or:
TTD=ƒ(U)xe2x80x83xe2x80x83Eq.9
The theory goes on to say that the thermal resistance R, the inverse of U, can be described as the sum of all resistances in the path of heat flow from the steam to the circulating water, given by:
R={fraction (1/U)}=Ra+Rc+Rt+Rf+Rwxe2x80x83xe2x80x83Eq.10
where,
a is air;
c is condensate on tubes;
t is tube;
f is fouling and
w is circulating water.
Historically, much effort has gone into analytically describing each of these series resistances. The best characterized are Rw, Rf, and Rt. Values of Rc, dealing with condensate on the tubes, have gained a lot of attention with some success; and Ra essentially has been ignored with the exception of near equilibrium diffusion limited experimental measurements and its associated theory (C. L. Henderson, et al., xe2x80x9cFilm Condensation in the Presence of a Non-Condensable Gasxe2x80x9d, Journal of Heat Transfer, Vol. 91, pp. 447-450, August 1969). The latter generally is believed to be very complex (see Silver and Putman, supra) and limited data is available. The general belief is that small amounts of air will dramatically affect the heat transfer coefficient, resulting in an increase in the values of xcex94Tlm, TTD, and THW, without analytical description. The importance to the invention resides in part in that Ra is assumed to be treatable in a manner similar to tube fouling, as shown in Equation 10.
To examine the validity of the existing model, tests can be conducted. It should be expected that if a large number of power plant steam turbine condensers were tested under a normalized or similar condition, a common agreement or trend would exist in the measured heat transfer coefficient. These tests would confirm the usefulness of Equations 2 and 6 in describing performance of given condensers. Gray (J. L. Gray, Discussion, pp. 358-359; Silver supra) reports the determined heat transfer coefficients, using Equation 6, versus circulating water tube velocity for many clean tube condensers normalized to 60xc2x0 F. inlet circulating water. These data are shown in FIG. 2. According to the theory, all data should lie scattered about a neat curve as shown by Heat Exchange Institute (HEI) (Standards for Steam Surface Condensers, HEI, Eighth Edition, p. 9, 1984). Gray""s data show that this is not the case; he concluded that the measured variation indicates the need for an improved design basis. The degree of disagreement goes far beyond the subtle modification coefficients discussed elsewhere, (see Putman and HEI, both supra), which is the subject of modem theoretical endeavor.
Q is a measurable quantity and its value is relatively easy to ascertain. xcex94Tlm on the other hand is not so easy to determine. Investigators assume that it is the same for each tube in the condenser. For this to be the case, however, all tubes must have the same flow rate, equal (or no) internal fouling, and identical environments on the shell side. However, an overwhelming amount of data is available showing that this is not the case. Discharge temperature in the outlet water box may be non-uniform and tube exit temperatures vary as much as 10xc2x0 F. or more over large areas even though flow rate in each tube is the same. Work by Bell (R. J. Bell, et al., xe2x80x9cInvestigation of Condenser Deficiencies Utilizing State-of-the-Art Test Instrumentation and Modeling Techniques,xe2x80x9d Private communication) shows 20xc2x0 F. variations, which he attributes to xe2x80x9cair binding.xe2x80x9d The use of an overall average value of xcex94Tcw, should, however, be in proportion to Q. But, this does not guarantee that the form of Equation 2, 6, or 8 in determining the heat transfer coefficient value is valid.
Evaluators use the total tube surface area for the value of A in Equation 6. The form of Equation 6, however, reflects a different understanding for A. In this equation, A has the meaning that it is the useful area participating effectively as a heat exchange surface. That would include condensate on the tube surface and subcooled condensate drops or streams, in transit under the force of gravity, in the space between tubes. If any portion of the condenser is not involved significantly in condensing steam, and its numerical value is known, then the physical tube surface area A may be the wrong value to use in determining the active condenser heat transfer coefficient. The air binding, cited above, is an example. If the effects of air on U are not considered properly, then the effects of tube fouling on condenser performance becomes questionable.
Another limitation of the model is the lack of understanding of air in-leakage behavior within the shell side of the condenser. Instead of a xe2x80x9clittle amount of air affecting condenser performance,xe2x80x9d measurements show that as long as the air in-leakage is below the capacity of air removal equipment to remove air at a suction pressure compatible with the no air hotwell temperature equilibrium pressure, no excess turbine back pressure is experienced (J. W. Harpster, et al., xe2x80x9cTurbine Exhaust Excess Back pressure Reduction.xe2x80x9d FOMIS 38th Semiannual Conferencexe2x80x94Optimizing Station Performance, Clearwater Beach, Fla., Jun. 7-10, 1999). Very high air in-leakage can be prevented from affecting condenser performance simply by adding more exhausters. This means that the model developed, which shows air converging on tubes by virtue of scavenging by radially directed condensing vapor, is not valid throughout the condenser as some researchers may believe.
Further, when air in-leakage exceeds the capacity of the exhausters, the pressure begins to rise above an observed no air saturation level. Under these conditions, condenser performance is known to be adversely affected. Following from Equations 6, 9, and 10, the value of TTD should increase causing a rise in the Tv and a subsequent rise in hotwell temperature. In-plant measurements, however, do not always support a rise in hotwell temperature resulting from air in-leakage induced excess back pressure (see Harpster, id). This condition can sometimes be referred to as condensate subcooling. Added excess back pressure often appears as an air partial pressure above that of the hotwell temperature-driven water saturation vapor partial pressure. Further, there is no analytical description for the condenser pressure saturation response at low air in-leakage.
The importance of advanced instrumentation to directly measure assumed or unknown subsystem properties or characteristics of power plants, operating within the current market, is disclosed. These measurements are needed to quantify critical parameters, not only in power generation units with older control hardware, but also for those equipped with modern information systems, which may or may not contain simulation computations, for plant control and management. One such measurement is air in-leakage into the shell side of a steam surface condenser. This measurement, along with an understanding of its response to behavior of steam and non-condensables within the condenser space, forms one aspect of the present invention. This understanding provides the foundation for a comprehensive theoretical treatment of how air behaves in a condenser, and its effect on condenser performance.
The use of air in-leakage and condenser diagnostic instrumentation or multi-sensor probe (RheoVac(copyright) instrument, Intek, Inc., Westerville, Ohio) provides the ability to measure properties of the gases entering the vent line from the air removal section of a condenser. It will be shown that these data, along with other condenser operating parameters, can be combined to describe air passage within the condenser. Also described are the performance characteristics of the condenser as they are affected at different levels of air ingress. The impact of air in-leakage on excessive subcooling, resulting in high dissolved oxygen, will be presented. A practical control point for maintaining air in-leakage in operating plants will be disclosed from the viewpoint of minimizing dissolved oxygen and improving heat rate. A summary description of the functional manner in which the RheoVac instruments compute gas properties is provided since some important measurement data useful for power plant control and diagnostics derived by this instrument can now be made possible as a result of the model described in this application. It is now possible to use a temperature sensor at a new location, or a temperature sensor and a relative saturation sensor at another new location, to detect a condenser related source of excess back pressure (along with other normal plant measurements), by measuring the amount of subcooling at the exit of the air removal section.
Disclosed, then, is a method for operating a condenser of the type having a housing inside of which is disposed a bundle of circulating water tubes, a steam inlet allowing steam to flow inside the housing and contacting the tube bundle to reduce the steam to condensate, and the generation during operation of a stagnant air zone containing significant amount of air, wherein some air in-leakage can preferentially collect and remaining water vapor in the air zone becomes subcooled. A trough is placed beneath the stagnant air zone for collecting subcooled condensate generated there or falling through the stagnant air zone from above, unless otherwise diverted, and becoming high in dissolved oxygen concentration while transiting through this high air region. Collected subcooled condensate is transported by the trough to a pipe to said steam inlet preferably using a pump. The transported condensate is injected with an injector (spray device) for contacting with steam entering the condenser, whereby the injected condensate is heated by the steam for expelling dissolved oxygen in the injected condensate. Other means of reducing dissolved oxygen in condensate is also made clear. Advantageously, the outlet end of the tubes of the condenser is fitted with an array of temperature sensors extending through the expected stagnant air zone for direct measurement of its presence and/or size. A calibration of the condenser using a RheoVac(copyright) instrument may also be used to determine the extent of the stagnant zone.
Disclosed further, is a second condenser having the tube surface area of the size of the stagnant zone tube area, above, where noncondensable gases along with steam can enter from a smaller first condenser, which is devoid of a stagnant zone, for subcooling to take place and where condensate having a high concentration of oxygen can be collected and returned as spray in the steam entrance flow of the smaller first condenser.
Disclosed additionally is a temperature sensor located at the beginning of a vent line leaving a condenser for the purpose of making one of two measurements needed to determine the amount of subcooling in the condenser, to enable the determination of the number of tubes which have essentially lost their ability to condense steam due to buildup of air as a result of air in-leakage (or other noncondensables) in the condenser.
Disclosed further is a temperature sensor and a relative saturation sensor, located in the vent line after leaving the shell space of the condenser, which, if the gas therein was excessively subcooled before entering the vent line and subsequently becomes heated, while passing through the vest line, by the condensing steam, can now be used to determine the amount of subcooling at the vent inlet when compared to the condenser steam vapor temperature, thus determining the effect on the condenser by air buildup in the condenser as above.